Theorem 3ad2antl1 1183

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl1	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl2 1178	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  acexmid  6006  f1oen4g  6911  f1dom4g  6912  ordiso2  7213  addlocpr  7734  distrlem1prl  7780  distrlem1pru  7781  ltsopr  7794  addcanprlemu  7813  fzo1fzo0n0  10395  pfxsuffeqwrdeq  11246  prodfap0  12072  prodfrecap  12073  muldvds2  12344  dvds2add  12352  dvds2sub  12353  dvdstr  12355  qusaddvallemg  13382  mulgnnsubcl  13687  mulgpropdg  13717  ringidss  14008  lmodprop2d  14328  cnpnei  14909  upxp  14962  lgsval4lem  15706  clwwlkccatlem  16143  clwwlkccat  16144